Abstract—Offline signature verification is one of most

challenging area of pattern recognition. Many methods have

been introduced in literature to find whether a given signature

is genuine or forgery. In the proposed work, the signature

image is converted into time series data using linear scanning

method and then time series shapelets are identified to

distinguish genuine signatures from forged ones. The shapelets

are time series subsequences which are maximally

representative of a class. To compare the time series data, the

proposed method uses Mahalanobis distance measure. The

experimental results show that the method has great reduction

in equal error rate.

Index Terms—Mahalanobis distance measure, time series

data, time series shapelets, signatures.

I. INTRODUCTION

Notwithstanding efforts toward the dematerialization of

documents, the need for fast and accurate paper-based

document authentication is still growing in our society. The

field of biometrics is an important area of study as it offers

many advantages over more commonly used authentication

methods such as photo ID cards, magnetic strip cards etc.

Nowadays, biometric technologies are increasingly and more

frequently being used to ensure identity verification.

Signatures often incorporate complex geometric patterns that

make them a relatively secure means for authorization for

high security environments. For historical reasons, the

handwritten signature continues to be the most commonly

accepted form of transaction confirmation, as well as being

used in civil law contracts, acts of volition, or authenticating

one's identity. Some other offline signature verification

applications include the authentication of bank checks, ID

personal cards, administrative forms, formal agreements,

acknowledgement of services received, etc. Signature

verification has been a topic of intensive research during the

past several years due to the important role it plays in

numerous areas, including in financial applications.

Considering the large number of signatures verified daily

through visual inspection by people, the construction of a

robust and accurate automatic signature verification system

has many potential benefits for ensuring authenticity of

signatures and reducing fraud and other crimes. The goal of

an automatic signature verification system is to be able to

verify the identity of an individual, based on the analysis of

his or her signature through a process that discriminates a

Manuscript received March 5, 2014; revised June 20, 2014.

The authors are with Jawaharlal Nehru Technological University

Hyderabad, Hyderabad-500085, Andhra Pradesh, India (e-mail:

arathi.jntu@gmail.com, govardhan_cse@yahoo.co.in).

genuine signature from a forgery. The verification of human

signatures is particularly concerned with the improvement of

the interface between human beings and computers.

Depending on data acquisition mechanism, there are two

methods of signature verification - Online or Dynamic and

Offline or Static. Online method requires special set of

devices and instruments to capture the pen movements and

pressure over the paper at the same time of the writing. On

the other hand, the offline approach uses an optical scanner in

order to obtain a digital representation of the signature

composed of M × N pixels. In offline signature verification,

the signature image is considered as a discrete 2D function f(x,

y), where x = 0, 1, 2, …, M and y = 0, 1, 2, …, N denote the

spatial coordinates. The value of f in any (x, y) corresponds to

the grey level in that point [1]. Processing is done on the

scanned images.

Offline signature recognition is more difficult than online

as dynamic information are not available and it is difficult to

recover them from the offline images. But requirement of

acquiring the signature on some special arrangement makes

the online method unsuitable for many of the practical uses.

Offline has the advantage of using it in the same way as the

existing manual recognition method.

II. DEFINITIONS

A. Types of Forgeries

In signature verification systems, forgeries may be

classified into three basic types [2]:

Random forgery: The forger nor has access to the genuine

signature neither has any information about the author’s

name. Forger reproduces a random signature.

Simple forgery: The forger has no access to the sample of

the signature but he/she knows the author’s name and the

forger produces the signature in his/her own style.

Skilled forgery: The forger has access to the samples of

the genuine signature and thus he/she is able to reproduce it.

B. Error Rate

In signature verification systems, the performance is

evaluated in terms of error rates [2]. There are two types of

errors: False Rejection and False Acceptance. Also, there are

two types of error rates: False Rejection Rate (FRR) and

False Acceptance Rate (FAR). The false rejection rate (FRR)

is related to genuine signatures that were rejected by the

system; that is, classified as forgeries, whereas the false

acceptance rate (FAR) is related to forgeries that were

misclassified as genuine signatures. FRR is known as type 1

and FAR is known as type 2 error. The Average Error Rate

(AER) is the average of type 1 and type 2 errors [3]. Another

factor that determines the efficiency of the system is the

Equal Error Rate (EER). The EER is the location on a ROC

An Efficient Offline Signature Verification System

M. Arathi and A. Govardhan, Member, IACSIT

International Journal of Machine Learning and Computing, Vol. 4, No. 6, December 2014

533DOI: 10.7763/IJMLC.2014.V4.468

or Detection Error Trade-off curve where the FAR and FRR

are equal. Smaller the value of EER, better is the performance

of the system.

III. RELATED WORK

To improve the efficiency of the signature verification

systems, researchers have tried different methods with

various approaches. The offline signature verification system

proposed in [4] combines some statistical classifiers. This

signature verification system consisted of three steps – the

first step is to transform the original signatures using the

identity and four Gabor transforms, the second step is to

intercorrelate the analyzed signature with the similarly

transformed signatures of the learning database and then in

the third step verification of the authenticity of signatures by

fusing the decisions related to each transform.

An automatic off-line signature verification system

presented in [5] is built with several statistical techniques.

They used Hidden Markov Modeling (HMM) technique to

build a reference model for each local feature.

Another system proposed in [6] was based on global, grid

and texture features. For each one of the feature sets a special

two stage Perceptron OCON (one-class-one-network)

classification structure was implemented. In the first stage,

the classifier combined the decision results of the neural

networks and the Euclidean distance obtained using the three

feature sets. The results of the first-stage classifier feed a

second-stage radial base function (RBF) neural network

structure, which made the final decision.

A proposed system in [7] is based on a contour matching

algorithm. They used the geometrical properties of the

signature and considered the inevitable intrapersonal

variations for the user set.

To tackle the problem of detecting skilled forgeries in

off-line signature verification, [8] proposed an approach

based on a smoothness criterion. They observed that skilled

forgery signatures consisting of cursive graphic patterns are

less smooth on a detailed scale than the genuine ones.

Another system was proposed in [9] that has a

Cross-validation for Graph Matching based offline Signature

Verification (CGMOSV) algorithm. The dissimilarity

measure between two signatures in the database was

determined by (i) constructing a bipartite graph (ii) obtaining

complete matching in and (iii) finding minimum Euclidean

distance by Hungarian method.

Another work is based on the total energy that a writer uses

to create his/her signature as a global feature [10]. They

extracted energy information from the boundary of the whole

signature image.

Another work is based on three different kinds of feature

extractors - wavelet, curvelet and contourlet transform [11].

The curvature and orientation of a signature image was used

as feature. They utilized Support Vector Machine (SVM) as a

tool to evaluate the performance of the proposed methods.

In another paper [12], an off-line signature verification and

recognition system using the global, directional and grid

features of signatures is proposed. Global features used were

Signature area, Aspect Ratio of the signature, Maximum

horizontal histogram and maximum vertical histogram,

Horizontal and vertical center of the signature, Local maxima

numbers of the signature and Edge point numbers of the

signature. SVM was used for classification.

An offline signature verification system based on two

neural networks classifier and three features (global, texture

and grid) was proposed in [13]. The first NN classifier they

used was three Back Propagation NNs and the second

classifier consisted of two Radial Basis Function NNs.

The authors have designed a multi algorithmic signature

recognition system [14] considering the conventional

features like Number of pixels, Picture Width, Picture Height,

Horizontal max Projections, Vertical max Projections,

Dominant Angle-normalized, Baseline Shift etc.

Another system is based on score level fusion of distance

and orientation features of centroids [15]. The proposed

method used symbolic representation of offline signatures

using bi-interval valued feature vector.

An offline signature verification and forgery detection

proposed in [16] is based on fuzzy modeling that used a

model called the “Takagi–Sugeno (TS) model”. The TS

model involved structural parameters in its exponential

membership function.

From results obtained by the researchers in the field of

offline signature verification, it is noticed that the statistical

approach, (HMMs, Bayesian etc) can detect causal and

skilled forgeries. An acceptable recognition rate was reported

to be achieved using SVM [14]. Template matching is the

simplest and easiest approach, but it is rigid. So, it cannot

detect skilled forgery. Still it is suitable for detecting casual

forgeries from genuine signatures. When the signature image

is considered as a whole entity, the structural approach is

useful. But computational complexity in this approach is very

high as it requires large training sets. The performance is

reported to be better when number of training set is

sufficiently large. One additional advantage in using

structural pattern recognition is that this approach also

provides a description of the given pattern. Signatures with

most of the Indian scripted languages are usually long in

nature. For such long signatures, spectrum analysis approach

(like Curvelet, Contourlet or Wavelet transform) can be

better. In [12] authors have found that the contourlet

transform could extract better features. Neural Networks

based approaches have the advantages of being flexible and

adaptive [15]. Neural network based approaches are unified

approaches for feature extraction and classification and

flexible procedures for finding good, moderately nonlinear

solutions. Due to the advent of new learning algorithms and

seemingly low dependence on domain specific knowledge,

neural network is becoming more popular in the field of

pattern recognition. In addition, existing feature extraction

and classification algorithms can also be mapped on neural

network architectures for efficient (hardware)

implementation.

The closest work is that of time series classification using

shapelets [17]. Here, the authors classify the time series data

using shapelets. A shapelet is a subsequence of time series

data which represent a particular class. The algorithms that

are based on shapelets are interpretable, accurate and faster

than state-of-the-art classifiers. Shapelets are the local

features of time series data. Because shapelets are small in

size compared to the original data, algorithms that use

shapelets for classification, results in less time and space

International Journal of Machine Learning and Computing, Vol. 4, No. 6, December 2014

534

complexity. For classification with shapelets, decision trees

(binary) are used, where each nonleaf node represents a

shapelet and leaf nodes represent class labels. To know how

well the shapelet classifies the data, information gain [18] is

used.

IV. OFFLINE SIGNATURE VERIFICATION PROCESS

Offline signature verification is a pattern recognition

problem and a typical pattern recognition system has the

following steps [1], [19]: i) Data Acquisition ii)

Preprocessing iii) Feature Extraction iv) Classification v)

Performance Evaluation.

A. Data Acquisition

For offline signature verification system, images of the

signatures are scanned using a digital scanner. Scanned

images are stored digitally for offline processing.

B. Preprocessing

The purpose of pre-processing phase is to make signatures

standard and ready for feature extraction. The pre-processing

stage primarily involves some of the following steps: [3],

[19].

1. Noise reduction: A noise filter is applied to remove the

noise caused during scanning

2. Resizing: The image is cropped, to the bounding

rectangle of the signature

3. Binarization: Transformation from color to grayscale,

and then to binary

4. Thinning: The goal of thinning is to eliminate the

thickness differences of pen by making the image one pixel

thick.

5. Clutter Removal: Any unconnected black dots are

removed before processing. This is done by masking.

6. Skeletonization: Skeletonization is used to remove

selected foreground pixels from the binary image. So the

outcome is a representation of a signature pattern by a

collection of thin arcs and curves.

C. Feature Extraction

An ideal feature extraction technique extracts a minimal

feature set that maximizes interpersonal distance between

signature examples of various persons while minimizing

intrapersonal distance for those belonging to the same person

[1]. Features extracted for off-line signature verification can

be broadly divided into three main categories [20]:

Global Features

Local Features

Geometric Features

Global features: The signature is viewed as a whole and

features are extracted from all the pixels confining the

signature image.

Local features: Local features are extracted from a portion

or a limited area of the signature image [10]. These features

are calculated to describe the geometrical and topological

characteristics of local segments, such as position, tangent

direction, and curvature [21]. These features are generally

derived from the distribution of pixels of a signature, such as

local pixel density or slant.

Geometric features: These features describe the

characteristic geometry and topology of a signature and

preserve their global as well as local properties.

D. Classification

It evaluates the evidence presented in the values of the

features obtained from feature extraction and makes a final

decision for classification

E. Performance Evaluation

The efficiency of the signature verification system is

evaluated. It is done based on False Acceptance Rate and

False Rejection Rate.

V. PROPOSED METHOD

A. Converting Images to Time Series Data

To create the time series data for signature image, start at

the left of the image and consider each column of pixels in

turn. The value at each time is just the number of dark pixels

in that column. This process is known as linear scanning.

Time series analysis is only sensitive to an object’s

shape. It is invariant to colors and internal features. These

properties make time series analysis good for comparing

rigid objects, such as skulls, leaves, and handwriting. These

shapes do not change over time, so they will have similar

time series no matter when they are measured. Time series

analysis will not work on objects that can change their shapes

over time.

B. Finding Best Shapelet

Initially, all possible shapelets are generated ranging from

length 3 to length of the time series data [17]. To find best

shapelet, which classifies the data into genuine and forgery,

information gain is used. Once shapelet is found, it is inserted

into the decision tree. And the above process is repeated.

Because one shapelet is not sufficient to classify the data, a

number of shapelets are used which clearly distinguishes one

class from other. Each shapelet has its corresponding distance

threshold value, which divides the data into two sets. Hence,

the decision tree which is used as classifier is a binary

decision tree. The non-leaf nodes of the decision tree specify

shapelet and distance threshold; and leaf nodes specify the

class label. To classify a time series data, it is fed into

decision tree classifier, which moves it from the root node to

leaf node, which in turn gives the predicted class label.

C. Mahalanobis Distance Measure

In order to compare two time series data, the Mahalanobis

distance measure is used. The measure is a

descriptive statistic that provides a relative measure of a data

point's distance from a common point. It was introduced by P.

C. Mahalanobis in 1936 [22]. It is a unitless measure. It takes

into account the correlations of the data set and

is scale-invariant. Hence, it is a suitable measure for

classification.

Given a time series x(k)

, let the ith

data point be )(k

ix . First,

compute the(sample) covariance matrix C = (cij) of a family

of time series x(1)

, x(2)

,…, x(N)

of lengths n by

))(

)(1

)((

1

1jx

kjxN

k ixk

ixN

ijc

where N is the

number of instances and where ix is the average of the ith

International Journal of Machine Learning and Computing, Vol. 4, No. 6, December 2014

535

data point of the time series )1

)(1(

Nk

kix

Nix .

The Mahalanobis distance measure is a special case of the

generalized ellipsoid distance measure DM(x, y) = (x - y)T

M (x

- y) where M is proportional to the inverse of the covariance

matrix i.e., M C-1

. Though the Mahalanobis distance

measure is often defined by setting M to the inverse of the

covariance matrix (M = C-1

), it is convenient to normalize it

when possible so that the determinant of the matrix M is one:

M = 1

1

))(det( cc n where n is the length of the time series.

The Mahalanobis distance measure minimizes the sum of

distances between time series yx yxMD, ),( subject to a

regularization constraint on the determinant (det(M) = 1). In

this sense, it is optimal.

VI. EXPERIMENTAL RESULTS

The experiments are conducted on dataset containing 1287

questioned signatures and 646 reference signatures. The

questioned signatures contain both genuine and forged

signatures whereas reference signatures contain only genuine

signatures. The proposed method has shown Equal Error Rate

of 5.8%. As time series data along with shapelets has been

used for classification and Mahalanobis distance measure is

used for comparing two time series data, a good result for the

experiment has been observed.

VII. CONCLUSION

The offline signature verification system has been

developed by converting the images to time series data using

linear scanning and then the time series dataset is classified

using shapelets. The shapelets are time series subsequences

and are highly representative of a class. In order to compare

two time series data, Mahalanobis distance measure is used.

Mahalanobis distance measure is a good choice for

classification as it takes the correlation of data items into

consideration and is scale in-variant. Hence, it is obvious that

Mahalanobis distance measure will give more accurate

results. The experimental results have also shown that the

proposed method results in more accuracy.

REFERENCES

[1] L. Batista, D. Rivard, R. Sabourin, E. Granger, and P. Maupin, “State of the art in off-line signature verification,” in Pattern Recognition

Technologies and Applications: Recent Advances, 1st edition, B.

Verma, M. Blumenstein Eds., IGI Global, Hershey, 2007. [2] J. Coetzer, B. Herbst, and J. du Preez, “Off-line signature verification

using the discrete radon transform and a hidden Markov model,”

EURASIP Journal on Applied Signal Processing, 2004. [3] I. Guler and M. Meghdadi, “A different approach to off-line

handwritten signature verification using the optimal dynamic time

warping algorithm Digital Signal Processing,” Science Direct, vol. 18, pp. 940–950, 2008.

[4] J. B. Fasquel and M. Bruynooghe, “A hybrid opto-electronic method

for fast off-line handwritten signature verification,” International Journal on Document Analysis and Recognition, vol. 7, issue 1, pp.

56-98, March 2004.

[5] S. M. S. Ahmad, A. Shakil, M. A. Faudzi, R. M. Anwar, and M. A. M. Balbed, “A hybrid statistical modeling, normalization and inferencing

techniques of an off-line signature verification system,” in Proc. 2009

World Congress on Computer Science and Information Engineering,

2009, vol. 6, pp. 6-11.

[6] H. Baltzakis and N. Papamarkos, “A new signature verification technique based on a two-staged neural network classifier,”

Engineering Applications of Artificial Intelligence, vol. 14, pp. 95-103,

2001. [7] A. Bansal, D. Garg, and A. Gupta, “A pattern matching classifier for

offline signature verification,” in Proc. IEEE First International

Conference on Emerging Trends in Engineering and Technology, July 2008, pp. 1160-1163.

[8] B. Fang, Y. Y. Wang, C. H. Leung, Y. Y. Tang, P. C. K. Kwok, K. W.

Tse, and Y. K. Wong, “A smoothness index based approach for off-line signature verification,” in Proc. the Fifth International Conference on

Document Analysis and Recognition ICDAR‟99, 1999, pp. 785-787.

[9] A. C. Ramachandra, K. Pavithra, K. Yashasvini, K. B. Raja, K. R. Venugopal, and L. M. Patnaik, “Cross-validation for graph matching

based offline signature verification,” in Proc. India Conference

INDICON, 2008. [10] V. Nguyen, M. Blumenstein, and G. Leedham, “Global features for the

off-line signature verification problem,” in Proc. IEEE 10th

International Conference on Document Analysis and Recognition, July 2009, pp. 1300-1304.

[11] M. Fakhlai and H. Pourreza, “Off-line signature recognition based on

wavelet, curvelet and contourlet transforms,” in Proc. 8th WSEAS International Conference on Signal Processing and Computational

Geometry and Artificial Vision (ISCGAV‟08), Rhodes, Greece, August

20-22, 2008. [12] E. Özgündüz, T. Şentürk, and E. M. Karslıgil, “Off-line signature

verification and recognition by support vector machine,” 4-8

September, 2005, Antalya, Turkey, pp. 113-116. [13] M. A. Abdala and N. A. Yousif, “Off-line signature recognition and

verification based on artificial neural network,” Eng & Tech Journal,

vol. 27, no. 7, 2009. [14] V. A. Bharadi and H. B. Kekre, “Off-line signature recognition

systems,” International Journal of Computer Applications, vol. 1, no.

27, pp. 0975 – 8887, 2010. [15] H. N. Prakash and D. S. Guru, “Offline signature verification - an

approach based on score level fusion,” International Journal of

Computer Applications, vol. 1, no. 18, pp. 0975–8887, 2010. [16] M. Hanmandlu, M. Hafizuddin, M. Yusof, and V. K. Madasu,

“Off-line signature verification and forgery detection using fuzzy modeling,” Pattern Recognition, vol. 38, issue 3, pp. 341–356, 2005.

[17] L. Ye and E. Keogh, “Time Series Shapelets: a novel technique that

allows accurate, interpretable and fast classification,” Data Min. Knowl. Discov., vol. 22, no. 1-2, pp. 149-182, 2011.

[18] J. Han and M. Kamber, Data Mining: Concepts and Techniques,

Elsvier Publisher, 2nd edition. [19] R. O. Duda and P. E. Hart, Pattern Classification, 2nd edition, Wiley

India Private Limited, 2006.

[20] M. S. Arya and V. S. Inamdar, “A preliminary study on various off-line hand written signature verification approaches,” International Journal

of Computer Applications, vol. 1, no. 9, pp. 0975–8887, 2010.

[21] V. K. Madasu and B. C. Lovell, “An automatic off-line signature verification and forgery detection system,” in Pattern Recognition

Technologies and Applications: Recent Advances, B. Verma, M.

Blumenstein, Eds., 1st ed. IGI Global, Hershey, 2007. [22] P. C. Mahalanobis, "On the generalized distance in statistics,"

Proceedings of the National Institute of Sciences of India, vol. 2, no. 1,

pp. 49–55, 1936.

M. Arathi was born in Hyderabad, Andhra Pradesh,

India on 8 October, 1979. She received her B.E.(CSE)

from MVSREC, Hyderabad, Andhra Pradesh, India, in 2001, and M.Tech(CS), JNTUH, Hyderabad,

Andhra Pradesh, India, in 2008. Her major field of

study is data mining. She has worked as an assistant professor in Sant

Samarth Engineering College for 11 months. Now,

she is working as an assistant professor in JNTUH, Hyderabad, Andhra Pradesh, India. It is more than 10

years since she has been with JNTUH. She has helped the University in

finalizing syllabus for many subjects. She has 4 international journals, 6 international conference and 2 national publications.

Mrs. M. Arathi is an expert committee member for Institute for

Innovations in Science and Technology. She has been a judge for many paper presentation contests in JNTUH. She has subject expert for QTP

testing tool.

Author’s formal

photo

International Journal of Machine Learning and Computing, Vol. 4, No. 6, December 2014

536

A. Govardhan was born in Nalgonda, Andhra

Pradesh, India, on 10 March, 1970. He received his

B.E.(CSE) from Osmania University, Hyderabad, Andhra Pradesh in 1992, M.Tech(CS) from JNU,

New Delhi, India in 1994, and Ph.D(CS) from JNTU,

Hyderabad, Andhra Pradesh in 2003. His areas of research include databases, data mining and

information retrieval systems.

He is presently the director at SIT and Executive Council Member at Jawaharlal Nehru Technological

University Hyderabad (JNTUH), India. He has 2 Monographs and has

guided 125 M.Tech projects, 20 Ph.D thesis and has published 152 research

papers at journals/conferences including IEEE, ACM, Springer, Elsevier

and Inder Science. He has delivered more than 50 Keynote addresses. He

held several positions including the director of Evaluation, principal, HOD and students’ advisor.

Prof. A. Govardhan is a member on the editorial boards for eight

international journals, and a member of several Advisory & Academic Boards & Professional Bodies and a Committee Member for several

International and National Conferences. He is the chairman and a member

on several boards of studies of various universities and the chairman of CSI Hyderabad Chapter. He is the recipient of 21 international and national

awards.

Author’s formal

photo

International Journal of Machine Learning and Computing, Vol. 4, No. 6, December 2014

537